Triangle Centers and Properties

Professor Dave explains various lines and points related to triangles, including perpendicular bisectors, angle bisectors, medians, and altitudes. He describes how these lines intersect at specific points: the circumcenter, incenter, centroid, and orthocenter. Each point has unique properties, such as being equidistant from certain parts of the triangle. The video also covers how these concepts can be used to prove geometric theorems.

What is a perpendicular bisector in a triangle?

• A line that connects a vertex to the midpoint of the opposite side

• A line that is perpendicular to a side and divides it into two equal segments

• A line that divides an angle into two equal parts

• A line that extends from a vertex to the opposite side at any angle

Where do the three perpendicular bisectors of a triangle meet?

• At the orthocenter

• At the centroid

• At the circumcenter

• At the incenter

What is the circumcenter of a triangle?

• The point where the altitudes meet

• The point where the medians meet

• The point where the perpendicular bisectors meet

• The point where the angle bisectors meet

What is the incenter of a triangle?

• The point where the altitudes meet

• The point where the perpendicular bisectors meet

• The point where the angle bisectors meet

• The point where the medians meet

What is a median in a triangle?

• A line that extends from a vertex to the opposite side at any angle

• A line that divides an angle into two equal parts

• A line that is perpendicular to a side and divides it into two equal segments

• A line that connects a vertex to the midpoint of the opposite side

Where do the medians of a triangle meet?

• At the circumcenter

• At the centroid

• At the orthocenter

• At the incenter

What is the centroid of a triangle?

• The point where the medians meet

• The point where the angle bisectors meet

• The point where the altitudes meet

• The point where the perpendicular bisectors meet

What is an altitude in a triangle?

• A line that divides an angle into two equal parts

• A line that is perpendicular to a side and divides it into two equal segments

• A line that extends from a vertex to the opposite side at a right angle

• A line that connects a vertex to the midpoint of the opposite side

Where do the altitudes of a triangle meet?

• At the centroid

• At the orthocenter

• At the incenter

• At the circumcenter

Which point is always inside the triangle?

• Circumcenter

• Incenter

• None of the above

• Orthocenter